Leetcode Problem 1569. Number of Ways to Reorder Array to Get Same BST

Algorithm

1. Define a recursive function dfs(nums) that returns the number of valid permutations for a given subtree.
2. If nums has less than 3 elements, return 1 as there is only one way to form the BST.
3. Use the first element of nums as the root and partition the rest into left_nodes and right_nodes based on their values relative to the root.
4. Recursively call dfs on left_nodes and right_nodes to get the number of valid permutations for each subtree.
5. Calculate the binomial coefficient C(left+right, left) to determine the number of ways to interleave the two subtrees.
6. Multiply the results from steps 4 and 5 to get the total number of valid permutations for nums.
7. Use a dynamic programming table to efficiently calculate binomial coefficients.
8. Return the result of dfs(nums) modulo 10^9 + 7.